Metrics for Data.Random.Dice:roll from dice-0.1

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 7 to 5 computations (28.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

ival-sub: 0.0ms (0% of total)

ival-mult: 0.0ms (0% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample531.0ms (19.6%)

Results

387.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 138.0ms

ival-mult: 76.0ms (55.1% of total)

ival-sub: 47.0ms (34.1% of total)

const: 12.0ms (8.7% of total)

backward-pass: 3.0ms (2.2% of total)

Bogosity

preprocess315.0ms (11.6%)

Algorithm

2×	egg-herbie

Rules

1992×	`fmsub-define`
1904×	`sum4-define`
1738×	`sum3-define`
1722×	`fmm-def`
1712×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	33	13
2	89	12
3	229	12
4	667	12
5	2610	12
6	5287	12
7	7484	12
0	4	4
1	15	4
2	19	4
3	34	4
4	73	4
5	257	4
6	506	4
7	1108	4
8	3747	4
9	7852	4
0	8134	4

Stop Event

1×	iter limit
1×	node limit
1×	node limit

Calls

Call 1

Inputs
(- (* x x) 1)

Outputs
(- (* x x) 1)
(+.f64 (*.f64 x x) #s(literal -1 binary64))

Call 2

Inputs
(- (* x x) 1)
(- (* (neg x) (neg x)) 1)
(neg (- (* (neg x) (neg x)) 1))

Outputs
(- (* x x) 1)
(+ (square x) -1)
(- (* (neg x) (neg x)) 1)
(+ (square x) -1)
(neg (- (* (neg x) (neg x)) 1))
(- 1 (square x))

Symmetry

(abs x)

explain51.0ms (1.9%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`
-	-	`x`
-	-	`(*.f64 x x)`
-	-	`#s(literal 1 binary64)`

Results

33.0ms

512×

valid

Compiler

Compiled 30 to 14 computations (53.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-mult: 4.0ms (49.4% of total)

ival-sub: 3.0ms (37% of total)

const: 1.0ms (12.3% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 (*.f64 x x) #s(literal 1 binary64))

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify145.0ms (5.4%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(-.f64 (*.f64 x x) #s(literal 1 binary64))

Rules

1992×	`fmsub-define`
1722×	`fmm-def`
1712×	`fma-lowering-fma.f32`
1712×	`fma-lowering-fma.f64`
1664×	`fnmadd-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
1	15	8
2	19	8
3	34	8
4	73	8
5	257	8
6	506	8
7	1108	8
8	3747	8
9	7852	8
0	8134	8

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(- (* x x) 1)
(* x x)
x
1

Outputs
(- (* x x) 1)
(+.f64 (*.f64 x x) #s(literal -1 binary64))
(* x x)
(*.f64 x x)
x
1
#s(literal 1 binary64)

localize86.0ms (3.2%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 (*.f64 x x) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x x)

Results

81.0ms

256×

valid

Compiler

Compiled 12 to 5 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

ival-sub: 67.0ms (96.4% of total)

ival-mult: 2.0ms (2.9% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series1.0ms (0%)

Counts

2 → 24

Calls

Call 1

Inputs
#<alt (- (* x x) 1)>
#<alt (* x x)>

Outputs
#<alt -1>
#<alt (- (pow x 2) 1)>
#<alt (- (pow x 2) 1)>
#<alt (- (pow x 2) 1)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(- (* x x) 1)
0.0ms	x	@	0	(- (* x x) 1)
0.0ms	x	@	inf	(* x x)
0.0ms	x	@	0	(* x x)
0.0ms	x	@	-inf	(- (* x x) 1)

rewrite314.0ms (11.6%)

Algorithm

1×	batch-egg-rewrite

Rules

3176×	`/-lowering-/.f32`
3176×	`/-lowering-/.f64`
2130×	`fma-lowering-fma.f32`
2130×	`fma-lowering-fma.f64`
2042×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	30	6
2	171	6
3	1672	6
0	8279	6

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 285

Calls

Call 1

Inputs
(- (* x x) 1)
(* x x)

Outputs
(+.f64 (*.f64 x x) #s(literal -1 binary64))
(+.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) #s(literal 1 binary64)))) #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
(+.f64 #s(literal -1 binary64) (*.f64 x x))
(+.f64 (+.f64 x #s(literal -1 binary64)) (*.f64 x (+.f64 x #s(literal -1 binary64))))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))))))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
(+.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(+.f64 (.f64 (+.f64 x #s(literal -1 binary64)) x) (.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))
(+.f64 (.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) x))
(+.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) (.f64 #s(literal -1 binary64) (+.f64 x #s(literal 1 binary64))))
(+.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) (+.f64 x #s(literal -1 binary64)))
(+.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) #s(literal 1 binary64)))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))))) #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) #s(literal 1 binary64))))
(+.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (.f64 (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (-.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (+.f64 (.f64 x x) #s(literal 1 binary64))))))))) (fma.f64 (neg.f64 (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (-.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (+.f64 (.f64 x x) #s(literal 1 binary64)))))) (.f64 (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (-.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64)))))))))
(+.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))))))) (fma.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64)))) (.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64)))))))
(+.f64 (fma.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) #s(literal 1 binary64)))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))))) #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))) #s(literal 1 binary64))))
(+.f64 (fma.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (.f64 (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (-.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (+.f64 (.f64 x x) #s(literal 1 binary64))))))))) (fma.f64 (neg.f64 (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (-.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (+.f64 (.f64 x x) #s(literal 1 binary64)))))) (.f64 (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (-.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (+.f64 (.f64 x x) #s(literal 1 binary64)))))))))
(+.f64 (fma.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))))))) (fma.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64)))) (.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64)))))))
(+.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 x x) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) #s(literal 1 binary64)))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))))) #s(literal 1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) #s(literal 1 binary64))))
(+.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 x x) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (.f64 (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (-.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (+.f64 (.f64 x x) #s(literal 1 binary64))))))))) (fma.f64 (neg.f64 (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (-.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (+.f64 (.f64 x x) #s(literal 1 binary64)))))) (.f64 (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (-.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64)))))))))
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(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64)))) (-.f64 (.f64 (.f64 x x) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal -1 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (+.f64 (.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64)) (+.f64 (.f64 x x) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x))))))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))

simplify160.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

1672×	`fnmadd-define`
1562×	`-lowering-.f32`
1562×	`-lowering-.f64`
1460×	`fmsub-define`
1422×	`fma-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	88
1	18	65
2	43	65
3	97	65
4	320	65
5	570	65
6	1146	65
7	4624	65
0	8221	65

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

Inputs
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
-1
#s(literal -1 binary64)
(- (pow x 2) 1)
(+.f64 (*.f64 x x) #s(literal -1 binary64))
(- (pow x 2) 1)
(+.f64 (*.f64 x x) #s(literal -1 binary64))
(- (pow x 2) 1)
(+.f64 (*.f64 x x) #s(literal -1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(+.f64 (*.f64 x x) #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(+.f64 (*.f64 x x) #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(+.f64 (*.f64 x x) #s(literal -1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(+.f64 (*.f64 x x) #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(+.f64 (*.f64 x x) #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(+.f64 (*.f64 x x) #s(literal -1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval66.0ms (2.4%)

Compiler: Compiled 16308 to 778 computations (95.2% saved)

prune37.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	307	2	309
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	307	3	310

Accuracy

100.0%

Counts

310 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (*.f64 x x) #s(literal 1 binary64))
▶	51.2%	(*.f64 x x)
▶	50.0%	#s(literal -1 binary64)

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)

Rules

2×	`-lowering-.f32`
2×	`-lowering-.f64`
2×	`square-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	4	4
0	4	4

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
-1
(* x x)
x

Outputs
-1
#s(literal -1 binary64)
(* x x)
(*.f64 x x)
x

localize17.0ms (0.6%)

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)

Results

12.0ms

256×

valid

Compiler

Compiled 7 to 4 computations (42.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-mult: 3.0ms (85.9% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series0.0ms (0%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (* x x)>

Outputs
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(* x x)
0.0ms	x	@	inf	(* x x)
0.0ms	x	@	-inf	(* x x)

rewrite151.0ms (5.6%)

Algorithm

1×	batch-egg-rewrite

Rules

2200×	`pow-lowering-pow.f64`
2200×	`pow-lowering-pow.f32`
1438×	`prod-exp`
1304×	`-lowering-.f32`
1304×	`-lowering-.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	2	2
1	5	2
2	12	2
3	29	2
4	79	2
5	239	1
6	1690	1
7	1722	1
8	1856	1
9	3127	1
0	8463	1

Stop Event

1×	iter limit
1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(* x x)

Outputs
#s(literal 1 binary64)
x

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`pow-lowering-pow.f64`
2×	`pow-lowering-pow.f32`
2×	`-lowering-.f32`
2×	`-lowering-.f64`
2×	`unpow2`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	3	36
1	4	24
2	5	24
0	5	24

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

Calls

Call 1

Inputs
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval1.0ms (0.1%)

Compiler: Compiled 39 to 3 computations (92.3% saved)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	13	1	14
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	13	4	17

Accuracy

100.0%

Counts

17 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (*.f64 x x) #s(literal 1 binary64))
✓	51.2%	(*.f64 x x)
▶	4.5%	x
✓	50.0%	#s(literal -1 binary64)

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
x

Outputs
x

localize18.0ms (0.7%)

Results

15.0ms

256×

valid

Compiler

Compiled 3 to 2 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series0.0ms (0%)

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

rewrite10.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	3	3
Total	4	4

Accuracy

100.0%

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (*.f64 x x) #s(literal 1 binary64))
✓	51.2%	(*.f64 x x)
✓	4.5%	x
✓	50.0%	#s(literal -1 binary64)

Compiler

Compiled 25 to 14 computations (44% saved)

regimes6.0ms (0.2%)

Counts

4 → 1

Calls

Call 1

Inputs
#s(literal -1 binary64)
x
(*.f64 x x)
(-.f64 (*.f64 x x) #s(literal 1 binary64))

Outputs
(-.f64 (*.f64 x x) #s(literal 1 binary64))

Calls

3 calls:

2.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(-.f64 (*.f64 x x) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes8.0ms (0.3%)

Counts

3 → 2

Calls

Call 1

Inputs
#s(literal -1 binary64)
x
(*.f64 x x)

Outputs
#s(literal -1 binary64)
(*.f64 x x)

Calls

2 calls:

5.0ms	x
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.4%	2	`x`
99.4%	2	`(*.f64 x x)`

Compiler

Compiled 6 to 3 computations (50% saved)

regimes2.0ms (0.1%)

Counts

2 → 2

Calls

Call 1

Inputs
#s(literal -1 binary64)
x

Outputs
#s(literal -1 binary64)
x

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
52.9%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal -1 binary64)

Outputs
#s(literal -1 binary64)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
50.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.772746007252776e-13	889413.8295689352

Compiler

Compiled 10 to 7 computations (30% saved)

bsearch13.0ms (0.5%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	4.2103990395837493e-7	943.0873923284815

Results

7.0ms

144×

valid

Compiler

Compiled 64 to 52 computations (18.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-sub: 1.0ms (45.5% of total)

ival-mult: 1.0ms (45.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`mul-1-neg_binary64`
2×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	15	22
2	18	22
3	23	22

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 (*.f64 x x) #s(literal 1 binary64))
(if (<=.f64 (.f64 x x) #s(literal 3961408125713217/19807040628566084398385987584 binary64)) #s(literal -1 binary64) (.f64 x x))
(if (<=.f64 x #s(literal 1 binary64)) #s(literal -1 binary64) x)
#s(literal -1 binary64)

Outputs
(-.f64 (*.f64 x x) #s(literal 1 binary64))
(+.f64 (*.f64 x x) #s(literal -1 binary64))
(if (<=.f64 (.f64 x x) #s(literal 3961408125713217/19807040628566084398385987584 binary64)) #s(literal -1 binary64) (.f64 x x))
(if (<=.f64 x #s(literal 1 binary64)) #s(literal -1 binary64) x)
#s(literal -1 binary64)

soundness675.0ms (25%)

Rules

2200×	`pow-lowering-pow.f64`
2200×	`pow-lowering-pow.f32`
1672×	`fnmadd-define`
1562×	`-lowering-.f32`
1562×	`-lowering-.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	2	2
1	5	2
2	12	2
3	29	2
4	79	2
5	239	1
6	1690	1
7	1722	1
8	1856	1
9	3127	1
0	8463	1
0	9	88
1	18	65
2	43	65
3	97	65
4	320	65
5	570	65
6	1146	65
7	4624	65
0	8221	65

Stop Event

1×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 39 to 21 computations (46.2% saved)

preprocess61.0ms (2.3%)

Remove: (abs x)
Compiler: Compiled 82 to 44 computations (46.3% saved)

Data.Random.Dice:roll from dice-0.1

analyze0.0ms (0%)

sample531.0ms (19.6%)

preprocess315.0ms (11.6%)

explain51.0ms (1.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify145.0ms (5.4%)

localize86.0ms (3.2%)

series1.0ms (0%)

rewrite314.0ms (11.6%)

simplify160.0ms (5.9%)

eval66.0ms (2.4%)

prune37.0ms (1.4%)

simplify5.0ms (0.2%)

localize17.0ms (0.6%)

series0.0ms (0%)

rewrite151.0ms (5.6%)

simplify5.0ms (0.2%)

eval1.0ms (0.1%)

prune2.0ms (0.1%)

simplify3.0ms (0.1%)

localize18.0ms (0.7%)

series0.0ms (0%)

rewrite10.0ms (0.4%)

simplify3.0ms (0.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes6.0ms (0.2%)

regimes8.0ms (0.3%)

regimes2.0ms (0.1%)

regimes1.0ms (0.1%)

bsearch0.0ms (0%)

bsearch13.0ms (0.5%)

simplify8.0ms (0.3%)

soundness675.0ms (25%)

preprocess61.0ms (2.3%)

end0.0ms (0%)

Profiling